Abstract

Purpose:

To propose a simple model to explain the origin of ghost markers in marker-based optical tracking systems (OTS) and to develop retrospective strategies to detect and eliminate ghost markers.

Methods:

In marker-based OTS, ghost markers are virtual markers created due to the cross-talk between the two camera sensors, which can lead to system execution failure or inaccuracy in patient tracking. As a result, the users have to limit the number of markers and avoid certain marker configurations to reduce the chances of ghost markers. In this work, the authors propose retrospective strategies to detect and eliminate ghost markers. The two camera sensors were treated as mathematical points in space. The authors identified the coplanar within limit (CWL) condition as the necessary condition for ghost marker occurrence. A simple ghost marker detection method was proposed based on the model. Ghost marker elimination was achieved through pattern matching: a ghost marker-free reference set was matched with the optical marker set observed by the OTS; unmatched optical markers were eliminated as either ghost markers or misplaced markers. The pattern matching problem was formulated as a constraint satisfaction problem (using pairwise distances as constraints) and solved with an iterative backtracking algorithm. Wildcard markers were introduced to address missing or misplaced markers. An experiment was designed to measure the sensor positions and the limit for the CWL condition. The ghost marker detection and elimination algorithms were verified with samples collected from a five-marker jig and a nine-marker anthropomorphic phantom, rotated with the treatment couch from −60° to +60°. The accuracy of the pattern matching algorithm was further validated with marker patterns from 40 patients who underwent stereotactic body radiotherapy (SBRT). For this purpose, a synthetic optical marker pattern was created for each patient by introducing ghost markers, marker position uncertainties, and marker displacement.

Results:

The sensor positions and the limit for the CWL condition were measured with excellent reproducibility (standard deviation ≤ 0.39 mm). The ghost marker detection algorithm had perfect detection accuracy for both the jig (1544 samples) and the anthropomorphic phantom (2045 samples). Pattern matching was successful for all samples from both phantoms as well as the 40 patient marker patterns.

Conclusions:

The authors proposed a simple model to explain the origin of ghost markers and identified the CWL condition as the necessary condition for ghost marker occurrence. The retrospective ghost marker detection and elimination algorithms guarantee complete ghost marker elimination while providing the users with maximum flexibility in selecting the number of markers and their configuration to meet their clinic needs.